Pascal’s Wager is a classic for those who want to argue about the existence of God, but now, according to Peter L. Bernstein, of the New York Times, we should be using it for financial risk calculations. Say what?
Bernstien starts out fine:

For example, the average annual inflation rate in the United States was only 1.4 percent from the end of 1954 to the end of 1965. But in 1965, who could have imagined that inflation would average nearly five times that rate over the next 15 years?

That observation sounds like a platitude, but consider the kinds of questions it provokes. How will we deal with surprises — outcomes different from what we expect? What are the consequences of being wrong in our expectations? This is the point when risk management begins to live up to its real meaning. Risk means the chance of being wrong — not always in an adverse direction, but always in a direction different from what we expected.

Yes, yes. Risk is about what is not expected, and many financial fiasco’s have been the fault of or worsened by risk in a direction not considered. But then we get to the good stuff. What should we do about this? We should learn from Pascal’s Wager:

The key word is “consequences.” I learned this lesson many years ago from studying Blaise Pascal, a French mathematical genius in the 17th century who spelled out the laws of probability more clearly than anyone before him. This was a thunderclap of an insight that, for the first time, gave humanity a systematic way of thinking about the future.

Pascal was both a gambler and a religious zealot. One day he asked himself how he would handle a bet on whether “God is or God is not.” Reason could not answer. But, he said, we can choose between acting as though God is or acting as though God is not.

Suppose we bet that God is, and we lead a life of virtue and abstinence, and then the day of reckoning comes and we discover that there is no God. Well, life was still tolerable even if less fun than we might have liked. Here, the consequences of being wrong would be acceptable to most people.

Suppose, however, we bet that God is not, and lead a life of lust and sin, and then it turns out that God is. Now being wrong has put us into big trouble.

Which leads me to propose the new investment strategy, based on the brilliant guy with a triangle named after him. I call it Lacsap’s Wager:

Lacsap’s Wager by Dave Bacon

Lacsap was both a puritan and a religious moderate. One day he asked himself how he would handle how to invest for his retirement. Reason could not answer. But, he said, we can choose between two choices: invest the money for retirement or not invest the money for retirement.

Suppose we choose to not invest the money, and we lead a life of partying and hedonism, and then the day of reckoning comes and we discover that we’re old and can’t take care of ourselves. Well, life was still pretty damn fun and we can always go on the dole. Here, the consequences of being wrong would be acceptable to most people.

Suppose, however, we invest all of our money for retirement, and lead a life of thrift, and then it turns out that the entire financial world collapses. Now being wrong has put us into big trouble. We have both lost all of our money, and we didn’t get to enjoy it while we had it.

In all seriousness I agree with Bernstein that some narrow definitions of risk can lead to disaster. But I’m a little more skeptical that Pascal’s Wager will give me any deep insight into how to deal with this problem.

Comments

I would be extremely surprised to hear that game theory is not already applied to economics. As Pascal’s wager is just an application of game theory (with some pretty terrible assumptions) then it seems that looking at the wager specifically would only detract from the more general technique.

I think that Pascal’s Wager is a very illustrative case for understanding risks, although it seems that very few people draw what I consider to be the correct conclusions about it.

There are two lessons to be learned from a Pascal’s Wager type thought experiment, and Pascal only mentions one of them. The first lesson is: Don’t just go with the best theory, take into account alternative theories in assessing risk.

The way that many people go about making decisions that involve uncertainty is to first figure out which theory you should believe, and then do what that theory says is best. That strategy has the benefit of simplicity, but it’s not actually the best strategy. To take an example, suppose that the best theory available for cancer, or nuclear power, or whatever, says that course of action X is perfectly safe. Then should you follow course of action X? Not necessarily. It depends on how robust is the prediction that X is safe. Suppose that there are two competing theories about X. The first theory says that X is perfectly safe, and the second theory, which is also respectable, but is a minority opinion, says that X will result in the complete destruction of human civilization. Do you go with the “best” theory in this case? No, you really shouldn’t. If you believe that there is a nonnegligible possibility that the minority opinion is right, you should go with it in this case.

The second lesson that should be learned from Pascal’s Wager, but is almost always glossed over, is that in order to take into account alternative theories, you must use a subjective notion of likelihood. The best way to do this is Bayesian probability, but if you don’t want to go all the way, you should at least have a rough way to partition theories into “what’s most likely true”, “respectable alternatives”, “possible, but unlikely alternatives”, and “crackpot theories not worth considering”. This kind of grouping is necessarily subjective, because you need a theory to compute objective probabilities, but you’re trying to decide what theory to go with.

In Pascal’s original wager, he decided to only give serious consideration to two possibilities: (1) There is no God, and no afterlife, or (2) The full Christian story of God and Heaven is correct. Of course, his dismissing other possibilities (that the Hindus were correct, or that there is a God, but He wants us to behave badly) was completely subjective. He had no real basis for deciding that. Different people would have different alternatives, and would give different weights to them. But unless you are 100% certain of whatever theory you believe, the best strategy is to take into account theories you don’t believe.

Lacsap was both a puritan and a religious moderate. One day he asked himself how he would handle how to invest for his retirement. Reason could not answer. But, he said, we can choose between two choices: invest the money for retirement or not invest the money for retirement.

Suppose we choose to not invest the money, and we lead a life of partying and hedonism, and then the day of reckoning comes and we discover that we’re old and can’t take care of ourselves. Well, life was still pretty damn fun and we can always go on the doll [you mean like, inflatable?]. Here, the consequences of being wrong would be acceptable to most people.

Suppose, however, we invest all of our money for retirement, and lead a life of thrift, and then it turns out that the entire financial [financial what?] collapses. Now being wrong has put us into big trouble. We have both lost all of our money, and we didn’t get to enjoy it while we had it.

A devout Christian once tried to persuade me with Pascal’s argument, ie, convince me to believe in God and accept Christ just in case I turn out to be wrong when I die. I’ve always found such “rational” arguments in favor of being a practicing Christian kind of offensive and obtuse. One might as well respond: “I’ll wait, and see if Satan offers me a better deal.”

The bane of genuine rationality (not to mention wisdom and decency) is the indiscriminate and unreflective use of superficially rational argumentation. A lot of people indulge in it mainly because clever argumentation is their stock in trade.

Yes, in fact Nash’s Nobel Prize was actually in economics and not math for exactly that – applying game theory to economics.

As for investing, this all assumes one has enough money to invest. While that may sound cynical, note that my monthly fuel bill for heating my house last year was $299 (I have one of those plans that evens out the payments). The notice just came from my oil company (one of the largest in Maine) that next year’s plan will cost $644 per month.

If I get any money to invest, I’m buying oil company stock. I figure at this point that’s simply a way to get my own money back.

Well I think calling Pascal’s wager “game theory” is a bit of stretch. To me it just basic probability. If you put in infinite value for one of your random variables you can get some pretty silly results.

I’m not suggesting that it is game theory in and of its self, but game theory certainly contains this kind of analysis as a specific case. I only brought it up because I find it weird that someone (i.e. Bernstein) would bring it up as a useful tool when there already is a more general tool already in use in the field that contains this as a specific case.

IF the wager on the existence of God is a 2-player zero-sum game between God and Pascal, THEN what is the Nash Equilibrium of the payoff matrix?

Descartes’s analysis is based on the possibility that the wager on the existence of God is a 3-player zero-sum game between God and Pascal and Satan, the latter maximizing mathematical disinformation by feeding false sense-impressions and false memories into the mind/soul of the human.

Rather than making spurious Bayesian estimates, Descartes looks for invariants of the dynamics of mind to mind mapping over time, and finds that these include “cogito ergo sum.” He also postulates a mind/body duality, partially to dull the pain of his being an unloved motherless child. It was a radical step, especially for a Jesuit-educated genius, to base a philosophy on doubt rather than on faith.

I’m guessing that he arrived at this in the Jesuit school by gazing long and hard at a crucifix, abstracting away the tortured body with which he empathized, and leaving just a crossed x- and y-axis.

NOW we can ask Dave about the interesting results (cited in several refereed papers by myself and Prof. Philip V. Fellman) that quantum games, in which players and/or referees may be entangled, have additional Nash equilibria not possible when the games are embedded in classical physics.

Are humans and God entangled? And what about that 3rd player, the Father of Lies? Remember his bet with God over Job.

Pascal’s Wager was about whether God exists. To view it as a game between Pascal and God (let’s leave Satan out of it for now), it’s a peculiar game. God’s moves consist of the decision whether to exist or not?

Daryl McCullough: yes, to a first order “God’s moves consist of the decision whether to exist or not” — but then gets more peculiar, as the game is repeated over and over. In theory, both Pascal and God re-assess the odds based on what they think the other is doing. Yes, we leave 3rd players out at this level of analysis, although one may have a referee. Whether the referee is more powerful than God because the referee exists is the question raised in Saint Anselm’s ontological argument for God’s existence, with or without the axiomatization by the mathematician Kurt Godel.

Note that even extremely simple games such as “Rock, Paper, Scissors” have been proven to have chaotic trajectories.

Theothermodynamics concludes: “You can’t win, you can’t break even, you can’t get out of the game, and readers of the Quantum Pontiff are dubious that it’s even a game.”

The application of game theory to economics goes back a lot further than Nash, to the early days of game theory itself. The seminal text was Theory of Games and Economic Behavior, published in 1944, by John von Neumann and (economist) Oskar Morgenstern.